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- Apply the De Almbert’s Ratio Test tothe given series. Possible answers are «convergent», «divergent», or «DeAlmbert’s Ratio Test gives no information».Suppose that the radius of convergence of the power series cn xn is R. What is the radius of convergence of the power series cn x7n ?Compute the values up to four decimal places of the following using Maclaurin's series: Arcsin 1
- Apply the Cauchy’s n-th Root Test tothe given series. Possible answers are «convergent», «divergent», or «Cauchy’sn-th Root Test gives no information».With the help of partial fraction or otherwise, find the series representation of a) about z = 0 for the region 2 < |z| < 3, b) about z = 2 for the region 1 < |z − 2|. (Hint: let w = z − 2.) In each case, write explicitly some non-vanishing terms to illustrate the series.Are the given series converges or diverges. Which tests can we use and how can we apply?
- State an appropriate series with which to use the Comparison or Limit Comparison Test to prove whether ∑n=1 oo 1/n+ln(n)) converges or diverges. Show all work.Construct a power series centered at x = 0.Where does the subsequence series Nk = 2kpi come from? While I know it's used to specify the set of solutions...how/why can we just pull it out and use it in this series?
- Does the series from n=1 to infiniity of ((n!)^3)/((3n)!) converge or diverge using the ratio test?In the eqation given as follows , use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods: see the equation as attached here :-1. Find the truncation error of the Maclaurin series sinx cosx given that is truncated into three (3) terms. See the picture below,,, hope it might help.